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Congruences between modular forms

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Abstract

We survey the connections between modular forms and representations of Galois groups that are predicted by the Langlands programme. We focus in particular on the applications of congruences between modular forms (through automorphy lifting theorems) to an improved understanding of these connections, including the author’s recent joint work with James Newton on the existence of the symmetric power liftings of Hilbert modular forms.

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  1. Department of Pure Mathematics and Mathematical Statistics, Wilberforce Road, Cambridge, UK

    Jack A Thorne

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Communicated by Chandrashekhar Khare.

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Thorne, J.A. Congruences between modular forms. Proc Math Sci 134, 9 (2024). https://doi.org/10.1007/s12044-024-00776-4

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